Degeneracy at 1871 keV in Cd 112 and implications for neutrinoless double electron capture

High-statistics $\\ensuremath{\\beta}$-decay measurements of $^{112}\\mathrm{Ag}$ and $^{112}\\mathrm{In}$ were performed to study the structure of the $^{112}\\mathrm{Cd}$ nucleus. The precise energies of the doublet of levels at 1871 keV, for which the ${0}^{+}$ member has been suggested as a possible daughter state following neutrinoless double electron capture of $^{112}\\mathrm{Sn}$, were determined to be 1871.137(72) keV (${0}_{4}^{+}$ level) and 1870.743(54) keV (${4}_{2}^{+}$ level). The nature of the ${0}_{4}^{+}$ level, required for the calculation of the nuclear matrix element that would be needed to extract a neutrino mass from neutrinoless double electron capture to this state, is suggested to be of intruder origin.